Probably it was some sort of my mistake because of me messing with autolayouts and storyboard but I found an answer.
You have to take care of this little guy in View Controller's Attribute Inspector asvi
It must be unchecked so the default contentInset wouldn't be set after any change. After that it is just adding one-liner to viewDidLoad:
[self.tableView setContentInset:UIEdgeInsetsMake(108, 0, 0, 0)]; // 108 is only example
Adjust Scroll View Insets